According to his biographer Isḥāq
Israeli, Zarqālī was a renowned instrument maker in Toledo, where
he taught himself astronomy. He worked for Ṣāʿid al‐Andalusī and was a leading figure
among Ṣāʿid's
group of astronomers. An anonymous Egyptian 14th‐century source (Kanz
al‐yawāqīt, Leiden Universiteitsbibliotheek, MS 468) quotes
a passage from Ṣāʿid's lost work entitled Ṭabaqāt al‐ḥukamāʾ, in which it is stated
that Zarqālī constructed an astronomical instrument, called al‐zarqāla,
for al‐Maʾmūn (1043–1075), the ruler of Toledo, in the year
1048/1049. It also says that Zarqālī wrote a treatise of 100 chapters
on its use. Zarqālī left Toledo between 1081, the beginning of the
reign of al‐Qādir, and 1085, the date of the conquest of the city
by Alfonso VI. He settled in Córdova, where he was protected by al‐Muʿtamid ibn ʿAbbād (1069–1091),
ruler of Seville.

There are
many variations of the name of Zarqālī, known as Azarquiel in Latin.
According to the Ṭabaqāt al‐umam
of Ṣāʿid al‐Andalusī,
he was known as walad al‐Zarqiyāl, from whence came the
Hispanicized form Azarquiel. The 13‐century biographer al‐Qifṭī maintains the expression
walad al‐Zarqiyāl in his Akhbār al‐ʿulamā”
bi‐akhbār al‐ḥukamāʾ.
Other readings quoted in Andalusian sources are al‐Zarqālluh, al‐Zarqāl,
or Ibn Zarqāl; readings such al‐Zarqāla and al‐Zarqālī
(sometimes al‐Zarqānī) seem to be classicized Eastern forms.

In his Jāmiʿal‐mabādiʾ
wa‐ʾl‐ghāyāt fī ʿilm
al‐mīqāt, an encyclopedic work on astronomy,
Abū al‐Ḥasan ʿAlī al‐Marrākushī (13th century) states that Zarqālī
was making observations in Toledo in 1061. This testimony is confirmed by
Ibn al‐Hāʾim al‐Ishbīlī
(flourished: 1204/1205) in his al‐Zīj al‐kāmil fī
al‐taʿālīm,
who attributes to Zarqālī 25 years of solar observations and 37
years of observations of the Moon. Al‐Qifṭī
says that his observations were used by Ibn
al‐Kammād.

One
can generally classify the contents of Zarqālī's work under four
main categories: astronomical theory, astronomical tables, magic, and astronomical
instruments.

The following four works by Zarqālī deal with astronomical
theory: (1) There is a treatise on the motion of the fixed stars, written
circa 1084/1085 and extant in Hebrew translation. It contains a study
of three different trepidation models, in the third of which variable precession
becomes independent of the oscillation of the obliquity of the ecliptic. (2)
There is a lost work summarizing 25 years of solar observations, probably
written circa 1075–1080. Its contents are known through secondary sources,
both Arabic and Latin. The title was either Fī sanat al‐shams
(On the solar year) or al‐Risāla al‐jāmiʿa
fī al‐shams (A comprehensive epistle on the Sun). In this work
Zarqālī established that the solar apogee had its own motion (of
about 1° in 279 Julian years) and devised a solar model with variable eccentricity
that became influential both in the Maghrib and in Latin Europe until the
time of Nicolaus
Copernicus. (3) There is an indirect reference to a theoretical work
entitled Maqāla fī ibṭāl
al‐ṭarīq allatī
salaka‐hā Baṭlīmūs fī istikhrāj
al‐buʿd
al‐abʿad
li‐ʿUṭārid (On the invalidity of
Ptolemy's
method to obtain the apogee of Mercury) mentioned by Ibn
Bājja. (4) There is a reference in Ibn al‐Hāʾim's
work to Zarqālī's lost writing (bi‐khaṭṭ
yadi‐hi, in his own hand) describing a correction to the
Ptolemaic lunar model. Ibn al‐Hāʾim understands this correction
as a result of the displacement of the center of the lunar mean motion in
longitude to a point on a straight line linking the center of the Earth with
the solar apogee, and at a distance of 24'. This model met with some success, for we find the same correction
in later Andalusian (Ibn al‐Kammād) and Maghribī (Ibn
Isḥāq,
Ibn al‐Bannāʾ)
zījes, although restricted to the calculation of eclipses and
the New Moon. It appears also in the Spanish canons of the first version of
the Alfonsine Tables and in a Provençal version of the tables of eclipses
of Gersonides, although in these tables the amount is given as 29' (either a copying error or a new estimation).

There are two works by Zarqālī dealing with astronomical
tables: (1) The Almanac is preserved in Arabic, Latin, and in an Alfonsine
translation. It is based on a Greek work calculated by a certain Awmātiyūs
in the 3rd or 4th century, although the solar tables seem to be the result
of the Toledan observations. Its purpose is to simplify the computation of
planetary longitudes using Babylonian planetary cycles (goal years).
(2) The Toledan Tables are known through a Latin translation. They
seem to be the result of an adaptation of the best available astronomical
material (i. e., Khwārizmī
and Battānī) to the coordinates
of Toledo that was made by a team led by Ṣāʿid and in which Zarqālī seems to have been a prominent member.
The mean‐motion tables are original and are the result of observations.
Ṣāʿid does not mention these tables although they had been completed before
the writing of the Ṭabaqāt in 1068.

The only
known magical work by Zarqālī is entitled Risāla fī
Ḥarakāt al‐kawākib
al‐sayyāra wa‐tadbīri‐hi (On the motions and influences
of planets), which is a treatise on talismanic magic using magic squares to
make talismans. It is preserved in two Arabic manuscripts, which contain two
different versions of the text. There is also a third one summarized in a
Latin translation.

Finally, Zarqālī has several works on astronomical instruments:
(1) There is a treatise on the construction of the armillary sphere, which
is preserved in an Alfonsine–Castilian translation. The original Arabic has
not survived. (2) There are two treatises on the construction (circa
1080/1081) and use (circa 1081/1082) of the equatorium, dedicated to
al‐Muʿtamid. Zarqālī's equatorium differs
from the earlier Andalusian model designed by Ibn
al‐Samḥ (circa 1025/1026) in
that it is an independent instrument that represents all the planetary deferents
and related circles on both sides of a single plate, while a second plate
bears all the epicycles. Mercury's deferent is represented as an ellipse.
(3) Marrākushī attributes to Zarqālī a sine quadrant with
movable cursor (majarra), which is a graphic scale of solar declination
with the solar longitude as argument. It is similar to the quadrant vetustissimus,
although in this quadrant the argument used is the date of the Julian year.
(4) There are two treatises on two variants of the same astronomical universal
instrument (al‐ṣaf īḥa
al‐mushtaraka li‐jamīʿal‐ʿurūḍ):
A 100‐chapter treatise on the use of the ṣaf īḥa (plate), called the zarqāliyya,
and another treatise of 60 chapters on the use of the ṣaf īḥa
shakkāziyya. In both instruments the stereographic
equatorial projection of the standard astrolabe is replaced by a stereographic
meridian projection onto the plane of the solstitial colure. In fact, it is
a dual projection corresponding to each of the Celestial Hemispheres, one
of which had its viewpoint at the beginning of Aries and the other at the
beginning of Libra. The end result was obtained by superimposing the projection
from Aries (turning it) onto the projection from Libra. The two variants of
the ṣaf īḥa differ slightly. The
zarqāliyya has, on its face, a double grid of equatorial and ecliptical
coordinates and a ruler horizon representing the horizontal ones. On its back,
in addition to the features proper to the astrolabe, it shows an orthographic
meridian projection of the sphere, a trigonometric quadrant, and a small circle
(named “of the Moon”) used to compute the geocentric distance of the Moon.
The shakkāziyya is a simplification of the zarqāliyya,
as Marrākushī states in his Jāmiʿ. On its front it bears a single grid of equatorial
coordinates and a grid of ecliptical ones reduced to the ecliptic line and
the circles of longitude marking the beginning of the zodiacal signs. The
back of this kind of ṣaf īḥa is the same as the back
of the astrolabe. There is an Alfonsine translation of the treatise on the
zarqāliyya, as well as several translations into Latin and Hebrew
of the treatise on the shakkāziyya.

Richter‐Bernburg,
Lutz (1987). “Ṣāʿid, the Toledan
Tables, and Andalusī Science.” In From Deferent to Equant: A Volume
of Studies in the History of Science in the Ancient and Medieval Near East
in Honor of E. S. Kennedy, edited by David A. King and George Saliba,
pp. 373–401. Annals of the New York Academy of Sciences. Vol. 500.
New York: New York Academy of Sciences.

——— (1987). “The Solar Theory of az‐Zarqāl: An Epilogue.”
In From Deferent to Equant: A Volume of Studies in the History of Science
in the Ancient and Medieval Near East in Honor of E. S. Kennedy, edited
by David A. King and George Saliba, pp. 513–519. Annals of the New York
Academy of Sciences. Vol. 500. New York: New York Academy of Sciences.